Visible Color. 700 (red) 580 (yellow) 520 (green)

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1 Color Theory

2 Physical Color Visible energy - small portion of the electro-magnetic spectrum Pure monochromatic colors are found at wavelengths between 380nm (violet) and 780nm (red) Color Theory - Center for Graphics and Geometric Computing, Technion 2

3 Visible Color Eye can perceive other colors as combination of several pure colors Most colors may be obtained as combination of small number of primaries Output devices exploits this phenomena 580 (yellow) 520 (green) 700 (red) Color Theory - Center for Graphics and Geometric Computing, Technion 3

4 Gamma Correction The CRT devices are not linear The amount of light emitted from the CRT screen is not linearly proportional to the voltage applied to its tube. If V min and V max are considered black and white intensities, respectively, (V min + V max ) / 2 is not 50% gray. Color Theory - Center for Graphics and Geometric Computing, Technion 4

5 Gamma Correction (cont d) A little bit of electronics: The electronic tube s (including CRT s) characteristic graph of the current I with respect to its voltage V is a polynomial function of the form I = kv β (for semiconductor devices, I = k e dv ) The power reaching the eye is W = IV =V kv β = kv γ Assume n intensity levels, I j, 1 j n on a linear scale. We seek the voltage require for each of these intensity levels, I j Color Theory - Center for Graphics and Geometric Computing, Technion 5

6 We have I j =kv j γ or Gamma Correction (cont d) V j = (I j / k) 1/γ This voltage computation that compensates for the nonlinearity of the CRT is denoted Gamma Correction Each CRT has its own γ value that the manufacturer provides with the CRT. Typically γ [2, 3] Color Theory - Center for Graphics and Geometric Computing, Technion 6

7 Non-Linearity of the Eye The human eye is sensitive to intensity of light logarithmically. Given four light sources of relative intensities of 1, 2, 9 and 10, the eye will distinguish between 1 and 2 much easier than between 9 and 10. It is therefore better to select our intensity levels on an exponential scale: I j+1 = r I j for some unknown constant r. Assume we have n = 256 intensity levels. Question: How can we derive r? Color Theory - Center for Graphics and Geometric Computing, Technion 7

8 Non-Linearity of the Eye (cont d) If I 0 =L 0 and I 255 =L 1, then, Or L 1 = I 255 = I 0 r 255 = L 0 r 255 r = (L 1 / L 0 ) 1/255 The factor of (L 1 / L 0 ) is know as the dynamic range of the CRT From practical tests r should be at most 1.01 for the eye to see the different gray levels continuously Color Theory - Center for Graphics and Geometric Computing, Technion 8

9 Mach Banding Another (very important to predators) property of animal and human eyes is the ability to perform edge/motion detection Named after Mach who discovered this phenomena in 1865, Mach banding could be seen in poor imagery Mach bands are seen in conjunction with C -1 and C 0 continuous surfaces. Color Theory - Center for Graphics and Geometric Computing, Technion 9

10 Dynamic Range The Human eye has a huge dymanic range See in full day light See in moon light 8 Bits has difficulties covering such a large range Modern graphics systems supports more bits per color (New NVidia/ATI graphics cards support 32 bits per color or 128 bits per pixel!) Algorithms were developed in recent years to support and merge several low range images into one image and display it on contemporary hardware Color Theory - Center for Graphics and Geometric Computing, Technion 10

11 Dynamic Range (cont d) Color Theory - Center for Graphics and Geometric Computing, Technion 11

12 Dynamic Range (cont d) Color Theory - Center for Graphics and Geometric Computing, Technion 12

13 Dynamic Range (cont d) Color Theory - Center for Graphics and Geometric Computing, Technion 13

14 Dynamic Range (cont d) Color Theory - Center for Graphics and Geometric Computing, Technion 14

15 The CIE Diagram (1931 & 1976) Universal standard Color (ignoring intensity) represented as affine combination of 3 primaries X, Y, Z x = X / (X + Y + Z). Same for y and z. Note x + y + z = 1 Y is selected to specifically follow the human-eye sensitivity. Z Y X 400nm 500nm 600nm 700nm Color Theory - Center for Graphics and Geometric Computing, Technion 15

16 CIE Diagram (1931 & 1976) Universal standard Color (ignoring intensity) represented as affine combination of 3 primaries X, Y, Z 3D vector (x,y,z) s. t. x+y+z=1 Colors are in the interior of rightangle unit triangle formed by two of the primaries Not all possible colors are visible Visible colors contained in horseshoe region Pure colors (hues) located on boundary of the region Color Theory - Center for Graphics and Geometric Computing, Technion 16

17 The CIE Diagram (cont d) In 3 space the plot of x, y, z looks as in the drawing on the right Not all possible colors are visible Visible colors contained in horse-shoe region Pure colors (hues) located on boundary of the region Consider the plot of x, y only once x, y are known so is z. 400nm Z Y X 500nm 600nm 700nm Color Theory - Center for Graphics and Geometric Computing, Technion 17

18 The CIE Diagram (cont d) Color white is point W=(1/3,1/3,1/3) Any visible color C is blend of a hue C and W Purity of color measured by its saturation: y D W C C d 1 d 2 x saturation(c) = d 1 d + 1 d 2 Complement of C is (only) other hue D on line through C and W Color Theory - Center for Graphics and Geometric Computing, Technion 18

19 The CIE Diagram (cont d) Color enhancement of an image increasing the saturation of the colors moves them towards the boundary of the visible region unsaturated saturated Color Theory - Center for Graphics and Geometric Computing, Technion 19

20 Color Gamuts Not every color output device is capable of generating all visible colors in CIE diagram y Usually color generated as affine combination of three primaries P, Q, R Possible colors bounded by triangle in XYZ space with vertices P, Q, R This triangle is called the output device s gamut P W Q R x Color Theory - Center for Graphics and Geometric Computing, Technion 20

21 Color Gamuts (cont d) Example: Primaries of low quality color monitor: y RED P = = GREEN Q BLUE R x Different color displays use different P, Q, R Same RGB image data, displayed on two monitors will look different! Question: Given P,Q,R of two color monitors and image I, what must be done in order for I to look the same on both monitors? Color Theory - Center for Graphics and Geometric Computing, Technion 21

22 The RGB Color Model Common in describing emissive color displays Red, Green and Blue are the primary colors in this model Color (including intensity) described as combination of primaries colormodels Color Theory - Center for Graphics and Geometric Computing, Technion 22

23 The RGB Color Model C G B W M Y colormixing R Col = rr + gg + bb r,g,b [0, 1] Yellow = Red+Green (1, 1, 0) Cyan = Green+Blue (0, 1, 1) Magenta = Red+Blue (1, 0, 1) White = Red+Green+Blue (1, 1, 1) Gray = 0.5 Red+0.5 Blue+0.5 Green (0.5, 0.5, 0.5) Main diagonal of RGB cube represents shades of gray Color Theory - Center for Graphics and Geometric Computing, Technion 23

24 The CMY Color Model Used mainly in color printing, where the primary colors are subtracted from the background white. Cyan, Magenta and Yellow primaries are the complements of Red, Green and Blue Primaries (dyes) subtracted from white paper which absorbs no energy Red = White-Cyan = White-Green-Blue (0, 1, 1) Green = White-Magenta = White-Red-Blue (1, 0, 1) Blue = White-Yellow = White-Red-Green (1, 1, 0) (r,g,b) = (1-c,1-m,1-y) C G Bl B Y R M Color Theory - Center for Graphics and Geometric Computing, Technion 24

25 The YIQ Color Model Human eye more sensitive to changes in luminance (intensity) than to changes in hue or saturation Luminance useful for displaying grayscale version of color signal (e.g. B&W TV) Luminance Y affine combination of R,G & B I & Q null blend (zero sum) of R,G & B Conversion 0.30 ( y, i, q) = ( r, g, b) Green component dominates luminance value Color Theory - Center for Graphics and Geometric Computing, Technion 25

26 The HSV Color Model People naturally mix colors based on Hue, Saturation and Value Resulting coordinate system is cylindrical H angle around V axis S [0,1] distance from V axis V [0,1] - luminance R Y M V 1.0 W G B colormodels 0 C Color Theory - Center for Graphics and Geometric Computing, Technion 26 H S

27 Color Quantization High-quality color resolution for images - 8 bits per primary = 24 bits = 16.7M different colors Reducing number of colors select subset (colormap/pallete) and map all colors to the subset Used for devices capable of displaying limited number of different colors simultaneously. E.g. an 8 bit display. R 0 quantization to 4 colors reps B Color Theory - Center for Graphics and Geometric Computing, Technion 27

28 Color Quantization Example 256 colors 64 colors 16 colors 4 colors Color Theory - Center for Graphics and Geometric Computing, Technion 28

29 Color Quantization Issues How are the representative colors chosen? Fixed representatives, image independent - fast Image content dependent - slow Which image colors are mapped to which representatives? Nearest representative - slow By space partitioning - fast R 0 quantization to 4 colors reps B Color Theory - Center for Graphics and Geometric Computing, Technion 29

30 Choosing the Representatives R uniform quantization to 4 colors image-dependent quantization to 4 colors R 0 B 0 B large quantization error small quantization error Color Theory - Center for Graphics and Geometric Computing, Technion 30

31 Uniform Quantization Fixed representatives - lattice structure on RGB cube Image independent - no need to analyze input image Some representatives may be wasted Fast mapping to representatives by discarding least significant bits of each component Common way for 24 8 bit quantization retain most significant bits of R, G and B components R uniform quantization to 4 colors 0 B large quantization error Color Theory - Center for Graphics and Geometric Computing, Technion 31

32 Median-Cut Quantization Image colors partitioned into n cells, s.t. each cell contains approximately same number of image colors Recursive algorithm Image representatives - centroids of image colors in each cell Image color mapped to rep. of containing cell not necessarily nearest representative R image-dependent quantization to 4 colors 0 B small quantization error Color Theory - Center for Graphics and Geometric Computing, Technion 32

33 Quantization uniform 256 colors median-cut 8 colors Color Theory - Center for Graphics and Geometric Computing, Technion 33

34 Binary Dithering Improve quality of quantized image by distributing quantization error original threshold dithered Color Theory - Center for Graphics and Geometric Computing, Technion 34

35 Binary Dithering B&W Threshold map upper half of gray-level scale to white and lower half to black If else 1 I ( i, j) > 2 I ( i, j) = 1; I ( i, Each pixel produces some quantization error Distribute quantization error use local threshold Use matrix of thresholds for each n n pixels If else end; I ( i, I ( i, I ( i, j) j) j) > = = M 1 0 mod n, Color Theory - Center for Graphics and Geometric Computing, Technion 35 ( i j) j = 0; mod n )

36 Dithering For four color input use 2 2 matrix (gray levels 0 to 255) threshold dither dither For 16 gray-levels use 4 4 matrix (gray levels 0 to 255) How to build n n matrix for n 2 gray-levels? Build matrix to generate 2 k final colors? Build 4 4 matrix from 256 gray-levels? Color Theory - Center for Graphics and Geometric Computing, Technion 36

37 Halftoning Displaying (printing) image on device with lower color range & higher resolution Most common in printing (high dpi) Pixels grouped together group pattern used to replace color-scale E.g. 2x2 blocks emulating 5 gray-scale levels Color Theory - Center for Graphics and Geometric Computing, Technion 37

38 Quantization + Dithering uniform uniform + dithering median-cut 8 colors median-cut + dithering Color Theory - Center for Graphics and Geometric Computing, Technion 38

39 Error Diffusion Reduce quantization error by propagating accumulated error from pixel to (some of) its neighbors in scanline order before thresholding FloydSteinberg(I) For x := 1 to XMax do For y := 1 to YMax do err := I(x,y)-(I(x,y)>128)*255; I(x,y) := (I(x,y)>128)*255; I(x+1,y) := I(x+1,y)+err*7/16; I(x-1,y+1) := I(x-1,y+1)+err*3/16; I(x,y+1) := I(x,y+1)+err*5/16; I(x+1,y+1) := I(x+1,y+1)+err*1/16; end end dither error-diffusion Note: error propagation weights must sum to one Color Theory - Center for Graphics and Geometric Computing, Technion 39

40 Error Diffusion (cont d) Here are more examples of FS dithering the Utah teapot: Color Theory - Center for Graphics and Geometric Computing, Technion 40

Physical Color. Color Theory - Center for Graphics and Geometric Computing, Technion 2

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